{"paper":{"title":"End Invariants for $\\SL(2,C)$ characters of the one-holed torus","license":"","headline":"","cross_cats":["math.DG","math.DS"],"primary_cat":"math.GT","authors_text":"Ser Peow Tan, Yan Loi Wong, Ying Zhang","submitted_at":"2005-11-25T05:29:09Z","abstract_excerpt":"We define and study the set ${\\mathcal E}(\\rho)$ of end invariants of a $\\SL(2,C)$ character $\\rho$ of the one-holed torus $T$. We show that the set ${\\mathcal E}(\\rho)$ is the entire projective lamination space $\\mathscr{PL}$ of $T$ if and only if (i) $\\rho$ corresponds to the dihedral representation, or (ii) $\\rho$ is real and corresponds to a SU(2) representation; and that otherwise, ${\\mathcal E}(\\rho)$ is closed and has empty interior in $\\mathscr{PL}$. For real characters $\\rho$, we give a complete classification of ${\\mathcal E}(\\rho)$, and show that ${\\mathcal E}(\\rho)$ has either 0, 1"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0511621","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/math/0511621/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}